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Sigma Series
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Sigma Series in Stochastics, Volume 1, 117--131
Heldermann Verlag 2004

White Noise Theory and Physics

Takeyuki Hida
Meijo University, Nagoya, Japan

White noise theory has extensively developed since it was started about a quarter of a century ago. The theory has been originated by physics, particularly by quantum dynamics, while mathematically it is mainly based on classical functional analysis. After its establishment, white noise analysis soon exhibited a major impact on the mathematical approach to quantum mechanics. Two ideas born at the beginning of the last century can be identified in the history of science paving the way for the development of white noise theory. In physics quantum mechanics opened a new "stochastic" chapter in exact sciences. In mathematics the proposal of Lebesgue integral made it possible to extend probability theory to cover almost any branch of science. Looking at these historical developments, the beauty of science on the one hand and the change of paradigm caused by stochastics on the other hand become visible.